Professor: Shlomo Libeskind
This seminar explores the development of geometry through the ages – from its practical origins through its deductive emphasis in ancient Greece, to Descartes’ invention of coordinate approach and the discovery of non-Euclidean Geometry in the early part of the 19th century. The seminar has a mathematical emphasis with focus on geometric constructions, coordinate geometry and transformational geometry. We explore the historical aspects, in part through viewing beautifully presented short video lectures from the Great Courses Company.
The seminar is accessible to any honors college student with a good knowledge of high school pre-calculus mathematics. We discuss strategies for approaching proofs and solving problems and guide students toward successfully solving unfamiliar problems on their own. We explore the following:
- How does one know how to begin a proof or a solution and how to proceed?
- Which approach is more promising and why?
- Are different solutions possible, and how do they compare?
We emphasize that proofs and solutions to problems don’t come “out of the blue” and discuss the thinking process leading to a proof or solution. Most of the evaluation (about 80%) is from weekly assignments and short class presentations from the assignments.